2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl_lp_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_space_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_vec_private.h>
24 #include <isl_range.h>
25 #include <isl_local.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_val_private.h>
29 #include <isl_config.h>
32 #define BASE pw_qpolynomial
34 #include <isl_list_templ.c>
36 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
39 case isl_dim_param
: return 0;
40 case isl_dim_in
: return dim
->nparam
;
41 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
46 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
54 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
59 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
61 return (struct isl_upoly_cst
*)up
;
64 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
69 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
71 return (struct isl_upoly_rec
*)up
;
74 /* Compare two polynomials.
76 * Return -1 if "up1" is "smaller" than "up2", 1 if "up1" is "greater"
77 * than "up2" and 0 if they are equal.
79 static int isl_upoly_plain_cmp(__isl_keep
struct isl_upoly
*up1
,
80 __isl_keep
struct isl_upoly
*up2
)
83 struct isl_upoly_rec
*rec1
, *rec2
;
91 if (up1
->var
!= up2
->var
)
92 return up1
->var
- up2
->var
;
94 if (isl_upoly_is_cst(up1
)) {
95 struct isl_upoly_cst
*cst1
, *cst2
;
98 cst1
= isl_upoly_as_cst(up1
);
99 cst2
= isl_upoly_as_cst(up2
);
102 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
105 return isl_int_cmp(cst1
->d
, cst2
->d
);
108 rec1
= isl_upoly_as_rec(up1
);
109 rec2
= isl_upoly_as_rec(up2
);
113 if (rec1
->n
!= rec2
->n
)
114 return rec1
->n
- rec2
->n
;
116 for (i
= 0; i
< rec1
->n
; ++i
) {
117 int cmp
= isl_upoly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
125 isl_bool
isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
126 __isl_keep
struct isl_upoly
*up2
)
129 struct isl_upoly_rec
*rec1
, *rec2
;
132 return isl_bool_error
;
134 return isl_bool_true
;
135 if (up1
->var
!= up2
->var
)
136 return isl_bool_false
;
137 if (isl_upoly_is_cst(up1
)) {
138 struct isl_upoly_cst
*cst1
, *cst2
;
139 cst1
= isl_upoly_as_cst(up1
);
140 cst2
= isl_upoly_as_cst(up2
);
142 return isl_bool_error
;
143 return isl_int_eq(cst1
->n
, cst2
->n
) &&
144 isl_int_eq(cst1
->d
, cst2
->d
);
147 rec1
= isl_upoly_as_rec(up1
);
148 rec2
= isl_upoly_as_rec(up2
);
150 return isl_bool_error
;
152 if (rec1
->n
!= rec2
->n
)
153 return isl_bool_false
;
155 for (i
= 0; i
< rec1
->n
; ++i
) {
156 isl_bool eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
161 return isl_bool_true
;
164 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
166 struct isl_upoly_cst
*cst
;
170 if (!isl_upoly_is_cst(up
))
173 cst
= isl_upoly_as_cst(up
);
177 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
180 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
182 struct isl_upoly_cst
*cst
;
186 if (!isl_upoly_is_cst(up
))
189 cst
= isl_upoly_as_cst(up
);
193 return isl_int_sgn(cst
->n
);
196 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
198 struct isl_upoly_cst
*cst
;
202 if (!isl_upoly_is_cst(up
))
205 cst
= isl_upoly_as_cst(up
);
209 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
212 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
214 struct isl_upoly_cst
*cst
;
218 if (!isl_upoly_is_cst(up
))
221 cst
= isl_upoly_as_cst(up
);
225 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
228 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
230 struct isl_upoly_cst
*cst
;
234 if (!isl_upoly_is_cst(up
))
237 cst
= isl_upoly_as_cst(up
);
241 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
244 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
246 struct isl_upoly_cst
*cst
;
250 if (!isl_upoly_is_cst(up
))
253 cst
= isl_upoly_as_cst(up
);
257 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
260 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
262 struct isl_upoly_cst
*cst
;
266 if (!isl_upoly_is_cst(up
))
269 cst
= isl_upoly_as_cst(up
);
273 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
276 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
278 struct isl_upoly_cst
*cst
;
280 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
289 isl_int_init(cst
->n
);
290 isl_int_init(cst
->d
);
295 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
297 struct isl_upoly_cst
*cst
;
299 cst
= isl_upoly_cst_alloc(ctx
);
303 isl_int_set_si(cst
->n
, 0);
304 isl_int_set_si(cst
->d
, 1);
309 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
311 struct isl_upoly_cst
*cst
;
313 cst
= isl_upoly_cst_alloc(ctx
);
317 isl_int_set_si(cst
->n
, 1);
318 isl_int_set_si(cst
->d
, 1);
323 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
325 struct isl_upoly_cst
*cst
;
327 cst
= isl_upoly_cst_alloc(ctx
);
331 isl_int_set_si(cst
->n
, 1);
332 isl_int_set_si(cst
->d
, 0);
337 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
339 struct isl_upoly_cst
*cst
;
341 cst
= isl_upoly_cst_alloc(ctx
);
345 isl_int_set_si(cst
->n
, -1);
346 isl_int_set_si(cst
->d
, 0);
351 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
353 struct isl_upoly_cst
*cst
;
355 cst
= isl_upoly_cst_alloc(ctx
);
359 isl_int_set_si(cst
->n
, 0);
360 isl_int_set_si(cst
->d
, 0);
365 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
366 isl_int n
, isl_int d
)
368 struct isl_upoly_cst
*cst
;
370 cst
= isl_upoly_cst_alloc(ctx
);
374 isl_int_set(cst
->n
, n
);
375 isl_int_set(cst
->d
, d
);
380 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
383 struct isl_upoly_rec
*rec
;
385 isl_assert(ctx
, var
>= 0, return NULL
);
386 isl_assert(ctx
, size
>= 0, return NULL
);
387 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
388 sizeof(struct isl_upoly_rec
) +
389 size
* sizeof(struct isl_upoly
*));
404 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
405 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
407 qp
= isl_qpolynomial_cow(qp
);
411 isl_space_free(qp
->dim
);
416 isl_qpolynomial_free(qp
);
421 /* Reset the space of "qp". This function is called from isl_pw_templ.c
422 * and doesn't know if the space of an element object is represented
423 * directly or through its domain. It therefore passes along both.
425 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
426 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
427 __isl_take isl_space
*domain
)
429 isl_space_free(space
);
430 return isl_qpolynomial_reset_domain_space(qp
, domain
);
433 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
435 return qp
? qp
->dim
->ctx
: NULL
;
438 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
439 __isl_keep isl_qpolynomial
*qp
)
441 return qp
? isl_space_copy(qp
->dim
) : NULL
;
444 /* Return a copy of the local space on which "qp" is defined.
446 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
447 __isl_keep isl_qpolynomial
*qp
)
454 space
= isl_qpolynomial_get_domain_space(qp
);
455 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
458 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
463 space
= isl_space_copy(qp
->dim
);
464 space
= isl_space_from_domain(space
);
465 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
469 /* Return the number of variables of the given type in the domain of "qp".
471 unsigned isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
472 enum isl_dim_type type
)
476 if (type
== isl_dim_div
)
477 return qp
->div
->n_row
;
478 if (type
== isl_dim_all
)
479 return isl_space_dim(qp
->dim
, isl_dim_all
) +
480 isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
481 return isl_space_dim(qp
->dim
, type
);
484 /* Given the type of a dimension of an isl_qpolynomial,
485 * return the type of the corresponding dimension in its domain.
486 * This function is only called for "type" equal to isl_dim_in or
489 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
491 return type
== isl_dim_in
? isl_dim_set
: type
;
494 /* Externally, an isl_qpolynomial has a map space, but internally, the
495 * ls field corresponds to the domain of that space.
497 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
498 enum isl_dim_type type
)
502 if (type
== isl_dim_out
)
504 type
= domain_type(type
);
505 return isl_qpolynomial_domain_dim(qp
, type
);
508 /* Return the offset of the first coefficient of type "type" in
509 * the domain of "qp".
511 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
512 enum isl_dim_type type
)
521 return 1 + isl_space_offset(qp
->dim
, type
);
523 return 1 + isl_space_dim(qp
->dim
, isl_dim_all
);
529 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
531 return qp
? isl_upoly_is_zero(qp
->upoly
) : isl_bool_error
;
534 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
536 return qp
? isl_upoly_is_one(qp
->upoly
) : isl_bool_error
;
539 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
541 return qp
? isl_upoly_is_nan(qp
->upoly
) : isl_bool_error
;
544 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
546 return qp
? isl_upoly_is_infty(qp
->upoly
) : isl_bool_error
;
549 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
551 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : isl_bool_error
;
554 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
556 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
559 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
561 isl_int_clear(cst
->n
);
562 isl_int_clear(cst
->d
);
565 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
569 for (i
= 0; i
< rec
->n
; ++i
)
570 isl_upoly_free(rec
->p
[i
]);
573 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
582 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
584 struct isl_upoly_cst
*cst
;
585 struct isl_upoly_cst
*dup
;
587 cst
= isl_upoly_as_cst(up
);
591 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
594 isl_int_set(dup
->n
, cst
->n
);
595 isl_int_set(dup
->d
, cst
->d
);
600 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
603 struct isl_upoly_rec
*rec
;
604 struct isl_upoly_rec
*dup
;
606 rec
= isl_upoly_as_rec(up
);
610 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
614 for (i
= 0; i
< rec
->n
; ++i
) {
615 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
623 isl_upoly_free(&dup
->up
);
627 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
632 if (isl_upoly_is_cst(up
))
633 return isl_upoly_dup_cst(up
);
635 return isl_upoly_dup_rec(up
);
638 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
646 return isl_upoly_dup(up
);
649 __isl_null
struct isl_upoly
*isl_upoly_free(__isl_take
struct isl_upoly
*up
)
658 upoly_free_cst((struct isl_upoly_cst
*)up
);
660 upoly_free_rec((struct isl_upoly_rec
*)up
);
662 isl_ctx_deref(up
->ctx
);
667 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
672 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
673 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
674 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
675 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
680 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
681 __isl_take
struct isl_upoly
*up2
)
683 struct isl_upoly_cst
*cst1
;
684 struct isl_upoly_cst
*cst2
;
686 up1
= isl_upoly_cow(up1
);
690 cst1
= isl_upoly_as_cst(up1
);
691 cst2
= isl_upoly_as_cst(up2
);
693 if (isl_int_eq(cst1
->d
, cst2
->d
))
694 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
696 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
697 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
698 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
701 isl_upoly_cst_reduce(cst1
);
711 static __isl_give
struct isl_upoly
*replace_by_zero(
712 __isl_take
struct isl_upoly
*up
)
720 return isl_upoly_zero(ctx
);
723 static __isl_give
struct isl_upoly
*replace_by_constant_term(
724 __isl_take
struct isl_upoly
*up
)
726 struct isl_upoly_rec
*rec
;
727 struct isl_upoly
*cst
;
732 rec
= isl_upoly_as_rec(up
);
735 cst
= isl_upoly_copy(rec
->p
[0]);
743 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
744 __isl_take
struct isl_upoly
*up2
)
747 struct isl_upoly_rec
*rec1
, *rec2
;
752 if (isl_upoly_is_nan(up1
)) {
757 if (isl_upoly_is_nan(up2
)) {
762 if (isl_upoly_is_zero(up1
)) {
767 if (isl_upoly_is_zero(up2
)) {
772 if (up1
->var
< up2
->var
)
773 return isl_upoly_sum(up2
, up1
);
775 if (up2
->var
< up1
->var
) {
776 struct isl_upoly_rec
*rec
;
777 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
781 up1
= isl_upoly_cow(up1
);
782 rec
= isl_upoly_as_rec(up1
);
785 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
787 up1
= replace_by_constant_term(up1
);
791 if (isl_upoly_is_cst(up1
))
792 return isl_upoly_sum_cst(up1
, up2
);
794 rec1
= isl_upoly_as_rec(up1
);
795 rec2
= isl_upoly_as_rec(up2
);
799 if (rec1
->n
< rec2
->n
)
800 return isl_upoly_sum(up2
, up1
);
802 up1
= isl_upoly_cow(up1
);
803 rec1
= isl_upoly_as_rec(up1
);
807 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
808 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
809 isl_upoly_copy(rec2
->p
[i
]));
812 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
813 isl_upoly_free(rec1
->p
[i
]);
819 up1
= replace_by_zero(up1
);
820 else if (rec1
->n
== 1)
821 up1
= replace_by_constant_term(up1
);
832 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
833 __isl_take
struct isl_upoly
*up
, isl_int v
)
835 struct isl_upoly_cst
*cst
;
837 up
= isl_upoly_cow(up
);
841 cst
= isl_upoly_as_cst(up
);
843 isl_int_addmul(cst
->n
, cst
->d
, v
);
848 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
849 __isl_take
struct isl_upoly
*up
, isl_int v
)
851 struct isl_upoly_rec
*rec
;
856 if (isl_upoly_is_cst(up
))
857 return isl_upoly_cst_add_isl_int(up
, v
);
859 up
= isl_upoly_cow(up
);
860 rec
= isl_upoly_as_rec(up
);
864 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
874 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
875 __isl_take
struct isl_upoly
*up
, isl_int v
)
877 struct isl_upoly_cst
*cst
;
879 if (isl_upoly_is_zero(up
))
882 up
= isl_upoly_cow(up
);
886 cst
= isl_upoly_as_cst(up
);
888 isl_int_mul(cst
->n
, cst
->n
, v
);
893 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
894 __isl_take
struct isl_upoly
*up
, isl_int v
)
897 struct isl_upoly_rec
*rec
;
902 if (isl_upoly_is_cst(up
))
903 return isl_upoly_cst_mul_isl_int(up
, v
);
905 up
= isl_upoly_cow(up
);
906 rec
= isl_upoly_as_rec(up
);
910 for (i
= 0; i
< rec
->n
; ++i
) {
911 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
922 /* Multiply the constant polynomial "up" by "v".
924 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
925 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
927 struct isl_upoly_cst
*cst
;
929 if (isl_upoly_is_zero(up
))
932 up
= isl_upoly_cow(up
);
936 cst
= isl_upoly_as_cst(up
);
938 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
939 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
940 isl_upoly_cst_reduce(cst
);
945 /* Multiply the polynomial "up" by "v".
947 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
948 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
951 struct isl_upoly_rec
*rec
;
956 if (isl_upoly_is_cst(up
))
957 return isl_upoly_cst_scale_val(up
, v
);
959 up
= isl_upoly_cow(up
);
960 rec
= isl_upoly_as_rec(up
);
964 for (i
= 0; i
< rec
->n
; ++i
) {
965 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
976 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
977 __isl_take
struct isl_upoly
*up2
)
979 struct isl_upoly_cst
*cst1
;
980 struct isl_upoly_cst
*cst2
;
982 up1
= isl_upoly_cow(up1
);
986 cst1
= isl_upoly_as_cst(up1
);
987 cst2
= isl_upoly_as_cst(up2
);
989 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
990 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
992 isl_upoly_cst_reduce(cst1
);
1002 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
1003 __isl_take
struct isl_upoly
*up2
)
1005 struct isl_upoly_rec
*rec1
;
1006 struct isl_upoly_rec
*rec2
;
1007 struct isl_upoly_rec
*res
= NULL
;
1011 rec1
= isl_upoly_as_rec(up1
);
1012 rec2
= isl_upoly_as_rec(up2
);
1015 size
= rec1
->n
+ rec2
->n
- 1;
1016 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
1020 for (i
= 0; i
< rec1
->n
; ++i
) {
1021 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
1022 isl_upoly_copy(rec1
->p
[i
]));
1027 for (; i
< size
; ++i
) {
1028 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
1033 for (i
= 0; i
< rec1
->n
; ++i
) {
1034 for (j
= 1; j
< rec2
->n
; ++j
) {
1035 struct isl_upoly
*up
;
1036 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
1037 isl_upoly_copy(rec1
->p
[i
]));
1038 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
1044 isl_upoly_free(up1
);
1045 isl_upoly_free(up2
);
1049 isl_upoly_free(up1
);
1050 isl_upoly_free(up2
);
1051 isl_upoly_free(&res
->up
);
1055 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
1056 __isl_take
struct isl_upoly
*up2
)
1061 if (isl_upoly_is_nan(up1
)) {
1062 isl_upoly_free(up2
);
1066 if (isl_upoly_is_nan(up2
)) {
1067 isl_upoly_free(up1
);
1071 if (isl_upoly_is_zero(up1
)) {
1072 isl_upoly_free(up2
);
1076 if (isl_upoly_is_zero(up2
)) {
1077 isl_upoly_free(up1
);
1081 if (isl_upoly_is_one(up1
)) {
1082 isl_upoly_free(up1
);
1086 if (isl_upoly_is_one(up2
)) {
1087 isl_upoly_free(up2
);
1091 if (up1
->var
< up2
->var
)
1092 return isl_upoly_mul(up2
, up1
);
1094 if (up2
->var
< up1
->var
) {
1096 struct isl_upoly_rec
*rec
;
1097 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
1098 isl_ctx
*ctx
= up1
->ctx
;
1099 isl_upoly_free(up1
);
1100 isl_upoly_free(up2
);
1101 return isl_upoly_nan(ctx
);
1103 up1
= isl_upoly_cow(up1
);
1104 rec
= isl_upoly_as_rec(up1
);
1108 for (i
= 0; i
< rec
->n
; ++i
) {
1109 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
1110 isl_upoly_copy(up2
));
1114 isl_upoly_free(up2
);
1118 if (isl_upoly_is_cst(up1
))
1119 return isl_upoly_mul_cst(up1
, up2
);
1121 return isl_upoly_mul_rec(up1
, up2
);
1123 isl_upoly_free(up1
);
1124 isl_upoly_free(up2
);
1128 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1131 struct isl_upoly
*res
;
1139 res
= isl_upoly_copy(up
);
1141 res
= isl_upoly_one(up
->ctx
);
1143 while (power
>>= 1) {
1144 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1146 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1153 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1154 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1156 struct isl_qpolynomial
*qp
= NULL
;
1162 if (!isl_space_is_set(space
))
1163 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1164 "domain of polynomial should be a set", goto error
);
1166 total
= isl_space_dim(space
, isl_dim_all
);
1168 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1173 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1182 isl_space_free(space
);
1184 isl_qpolynomial_free(qp
);
1188 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1197 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1199 struct isl_qpolynomial
*dup
;
1204 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1205 isl_upoly_copy(qp
->upoly
));
1208 isl_mat_free(dup
->div
);
1209 dup
->div
= isl_mat_copy(qp
->div
);
1215 isl_qpolynomial_free(dup
);
1219 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1227 return isl_qpolynomial_dup(qp
);
1230 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1231 __isl_take isl_qpolynomial
*qp
)
1239 isl_space_free(qp
->dim
);
1240 isl_mat_free(qp
->div
);
1241 isl_upoly_free(qp
->upoly
);
1247 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1250 struct isl_upoly_rec
*rec
;
1251 struct isl_upoly_cst
*cst
;
1253 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1256 for (i
= 0; i
< 1 + power
; ++i
) {
1257 rec
->p
[i
] = isl_upoly_zero(ctx
);
1262 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1263 isl_int_set_si(cst
->n
, 1);
1267 isl_upoly_free(&rec
->up
);
1271 /* r array maps original positions to new positions.
1273 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1277 struct isl_upoly_rec
*rec
;
1278 struct isl_upoly
*base
;
1279 struct isl_upoly
*res
;
1281 if (isl_upoly_is_cst(up
))
1284 rec
= isl_upoly_as_rec(up
);
1288 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1290 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1291 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1293 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1294 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1295 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1298 isl_upoly_free(base
);
1307 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1308 __isl_keep isl_mat
*div2
)
1313 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1314 div1
->n_col
>= div2
->n_col
,
1315 return isl_bool_error
);
1317 if (div1
->n_row
== div2
->n_row
)
1318 return isl_mat_is_equal(div1
, div2
);
1320 n_row
= div1
->n_row
;
1321 n_col
= div1
->n_col
;
1322 div1
->n_row
= div2
->n_row
;
1323 div1
->n_col
= div2
->n_col
;
1325 equal
= isl_mat_is_equal(div1
, div2
);
1327 div1
->n_row
= n_row
;
1328 div1
->n_col
= n_col
;
1333 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1337 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1338 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1343 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1346 struct isl_div_sort_info
{
1351 static int div_sort_cmp(const void *p1
, const void *p2
)
1353 const struct isl_div_sort_info
*i1
, *i2
;
1354 i1
= (const struct isl_div_sort_info
*) p1
;
1355 i2
= (const struct isl_div_sort_info
*) p2
;
1357 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1360 /* Sort divs and remove duplicates.
1362 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1367 struct isl_div_sort_info
*array
= NULL
;
1368 int *pos
= NULL
, *at
= NULL
;
1369 int *reordering
= NULL
;
1374 if (qp
->div
->n_row
<= 1)
1377 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1379 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1381 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1382 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1383 len
= qp
->div
->n_col
- 2;
1384 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1385 if (!array
|| !pos
|| !at
|| !reordering
)
1388 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1389 array
[i
].div
= qp
->div
;
1395 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1398 for (i
= 0; i
< div_pos
; ++i
)
1401 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1402 if (pos
[array
[i
].row
] == i
)
1404 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1405 pos
[at
[i
]] = pos
[array
[i
].row
];
1406 at
[pos
[array
[i
].row
]] = at
[i
];
1407 at
[i
] = array
[i
].row
;
1408 pos
[array
[i
].row
] = i
;
1412 for (i
= 0; i
< len
- div_pos
; ++i
) {
1414 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1415 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1416 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1417 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1418 2 + div_pos
+ i
- skip
);
1419 qp
->div
= isl_mat_drop_cols(qp
->div
,
1420 2 + div_pos
+ i
- skip
, 1);
1423 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1426 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1428 if (!qp
->upoly
|| !qp
->div
)
1442 isl_qpolynomial_free(qp
);
1446 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1447 int *exp
, int first
)
1450 struct isl_upoly_rec
*rec
;
1452 if (isl_upoly_is_cst(up
))
1455 if (up
->var
< first
)
1458 if (exp
[up
->var
- first
] == up
->var
- first
)
1461 up
= isl_upoly_cow(up
);
1465 up
->var
= exp
[up
->var
- first
] + first
;
1467 rec
= isl_upoly_as_rec(up
);
1471 for (i
= 0; i
< rec
->n
; ++i
) {
1472 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1483 static __isl_give isl_qpolynomial
*with_merged_divs(
1484 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1485 __isl_take isl_qpolynomial
*qp2
),
1486 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1490 isl_mat
*div
= NULL
;
1493 qp1
= isl_qpolynomial_cow(qp1
);
1494 qp2
= isl_qpolynomial_cow(qp2
);
1499 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1500 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1502 n_div1
= qp1
->div
->n_row
;
1503 n_div2
= qp2
->div
->n_row
;
1504 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1505 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1506 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1509 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1513 isl_mat_free(qp1
->div
);
1514 qp1
->div
= isl_mat_copy(div
);
1515 isl_mat_free(qp2
->div
);
1516 qp2
->div
= isl_mat_copy(div
);
1518 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1519 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1521 if (!qp1
->upoly
|| !qp2
->upoly
)
1528 return fn(qp1
, qp2
);
1533 isl_qpolynomial_free(qp1
);
1534 isl_qpolynomial_free(qp2
);
1538 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1539 __isl_take isl_qpolynomial
*qp2
)
1541 isl_bool compatible
;
1543 qp1
= isl_qpolynomial_cow(qp1
);
1548 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1549 return isl_qpolynomial_add(qp2
, qp1
);
1551 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1552 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1556 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1558 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1562 isl_qpolynomial_free(qp2
);
1566 isl_qpolynomial_free(qp1
);
1567 isl_qpolynomial_free(qp2
);
1571 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1572 __isl_keep isl_set
*dom
,
1573 __isl_take isl_qpolynomial
*qp1
,
1574 __isl_take isl_qpolynomial
*qp2
)
1576 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1577 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1581 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1582 __isl_take isl_qpolynomial
*qp2
)
1584 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1587 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1588 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1590 if (isl_int_is_zero(v
))
1593 qp
= isl_qpolynomial_cow(qp
);
1597 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1603 isl_qpolynomial_free(qp
);
1608 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1613 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1616 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1617 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1619 if (isl_int_is_one(v
))
1622 if (qp
&& isl_int_is_zero(v
)) {
1623 isl_qpolynomial
*zero
;
1624 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1625 isl_qpolynomial_free(qp
);
1629 qp
= isl_qpolynomial_cow(qp
);
1633 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1639 isl_qpolynomial_free(qp
);
1643 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1644 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1646 return isl_qpolynomial_mul_isl_int(qp
, v
);
1649 /* Multiply "qp" by "v".
1651 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1652 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1657 if (!isl_val_is_rat(v
))
1658 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1659 "expecting rational factor", goto error
);
1661 if (isl_val_is_one(v
)) {
1666 if (isl_val_is_zero(v
)) {
1669 space
= isl_qpolynomial_get_domain_space(qp
);
1670 isl_qpolynomial_free(qp
);
1672 return isl_qpolynomial_zero_on_domain(space
);
1675 qp
= isl_qpolynomial_cow(qp
);
1679 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1681 qp
= isl_qpolynomial_free(qp
);
1687 isl_qpolynomial_free(qp
);
1691 /* Divide "qp" by "v".
1693 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1694 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1699 if (!isl_val_is_rat(v
))
1700 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1701 "expecting rational factor", goto error
);
1702 if (isl_val_is_zero(v
))
1703 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1704 "cannot scale down by zero", goto error
);
1706 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1709 isl_qpolynomial_free(qp
);
1713 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1714 __isl_take isl_qpolynomial
*qp2
)
1716 isl_bool compatible
;
1718 qp1
= isl_qpolynomial_cow(qp1
);
1723 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1724 return isl_qpolynomial_mul(qp2
, qp1
);
1726 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1727 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1731 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1733 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1737 isl_qpolynomial_free(qp2
);
1741 isl_qpolynomial_free(qp1
);
1742 isl_qpolynomial_free(qp2
);
1746 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1749 qp
= isl_qpolynomial_cow(qp
);
1754 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1760 isl_qpolynomial_free(qp
);
1764 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1765 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1772 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1776 for (i
= 0; i
< pwqp
->n
; ++i
) {
1777 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1779 return isl_pw_qpolynomial_free(pwqp
);
1785 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1786 __isl_take isl_space
*domain
)
1790 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_zero(domain
->ctx
));
1793 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1794 __isl_take isl_space
*domain
)
1798 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_one(domain
->ctx
));
1801 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1802 __isl_take isl_space
*domain
)
1806 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_infty(domain
->ctx
));
1809 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1810 __isl_take isl_space
*domain
)
1814 return isl_qpolynomial_alloc(domain
, 0,
1815 isl_upoly_neginfty(domain
->ctx
));
1818 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1819 __isl_take isl_space
*domain
)
1823 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_nan(domain
->ctx
));
1826 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1827 __isl_take isl_space
*domain
,
1830 struct isl_qpolynomial
*qp
;
1831 struct isl_upoly_cst
*cst
;
1833 qp
= isl_qpolynomial_zero_on_domain(domain
);
1837 cst
= isl_upoly_as_cst(qp
->upoly
);
1838 isl_int_set(cst
->n
, v
);
1843 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1844 isl_int
*n
, isl_int
*d
)
1846 struct isl_upoly_cst
*cst
;
1851 if (!isl_upoly_is_cst(qp
->upoly
))
1854 cst
= isl_upoly_as_cst(qp
->upoly
);
1859 isl_int_set(*n
, cst
->n
);
1861 isl_int_set(*d
, cst
->d
);
1866 /* Return the constant term of "up".
1868 static __isl_give isl_val
*isl_upoly_get_constant_val(
1869 __isl_keep
struct isl_upoly
*up
)
1871 struct isl_upoly_cst
*cst
;
1876 while (!isl_upoly_is_cst(up
)) {
1877 struct isl_upoly_rec
*rec
;
1879 rec
= isl_upoly_as_rec(up
);
1885 cst
= isl_upoly_as_cst(up
);
1888 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1891 /* Return the constant term of "qp".
1893 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1894 __isl_keep isl_qpolynomial
*qp
)
1899 return isl_upoly_get_constant_val(qp
->upoly
);
1902 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1905 struct isl_upoly_rec
*rec
;
1913 rec
= isl_upoly_as_rec(up
);
1920 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1922 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1928 return isl_upoly_is_affine(rec
->p
[0]);
1931 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1936 if (qp
->div
->n_row
> 0)
1939 return isl_upoly_is_affine(qp
->upoly
);
1942 static void update_coeff(__isl_keep isl_vec
*aff
,
1943 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1948 if (isl_int_is_zero(cst
->n
))
1953 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1954 isl_int_divexact(f
, cst
->d
, gcd
);
1955 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1956 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1957 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1962 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1963 __isl_keep isl_vec
*aff
)
1965 struct isl_upoly_cst
*cst
;
1966 struct isl_upoly_rec
*rec
;
1972 struct isl_upoly_cst
*cst
;
1974 cst
= isl_upoly_as_cst(up
);
1977 update_coeff(aff
, cst
, 0);
1981 rec
= isl_upoly_as_rec(up
);
1984 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1986 cst
= isl_upoly_as_cst(rec
->p
[1]);
1989 update_coeff(aff
, cst
, 1 + up
->var
);
1991 return isl_upoly_update_affine(rec
->p
[0], aff
);
1994 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1995 __isl_keep isl_qpolynomial
*qp
)
2003 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2004 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
2008 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
2009 isl_int_set_si(aff
->el
[0], 1);
2011 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
2020 /* Compare two quasi-polynomials.
2022 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2023 * than "qp2" and 0 if they are equal.
2025 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2026 __isl_keep isl_qpolynomial
*qp2
)
2037 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2041 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2045 return isl_upoly_plain_cmp(qp1
->upoly
, qp2
->upoly
);
2048 /* Is "qp1" obviously equal to "qp2"?
2050 * NaN is not equal to anything, not even to another NaN.
2052 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2053 __isl_keep isl_qpolynomial
*qp2
)
2058 return isl_bool_error
;
2060 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2061 return isl_bool_false
;
2063 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2064 if (equal
< 0 || !equal
)
2067 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2068 if (equal
< 0 || !equal
)
2071 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
2074 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
2077 struct isl_upoly_rec
*rec
;
2079 if (isl_upoly_is_cst(up
)) {
2080 struct isl_upoly_cst
*cst
;
2081 cst
= isl_upoly_as_cst(up
);
2084 isl_int_lcm(*d
, *d
, cst
->d
);
2088 rec
= isl_upoly_as_rec(up
);
2092 for (i
= 0; i
< rec
->n
; ++i
)
2093 upoly_update_den(rec
->p
[i
], d
);
2096 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
2098 isl_int_set_si(*d
, 1);
2101 upoly_update_den(qp
->upoly
, d
);
2104 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2105 __isl_take isl_space
*domain
, int pos
, int power
)
2107 struct isl_ctx
*ctx
;
2114 return isl_qpolynomial_alloc(domain
, 0,
2115 isl_upoly_var_pow(ctx
, pos
, power
));
2118 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2119 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2121 if (isl_space_check_is_set(domain
) < 0)
2123 isl_assert(domain
->ctx
, pos
< isl_space_dim(domain
, type
), goto error
);
2125 if (type
== isl_dim_set
)
2126 pos
+= isl_space_dim(domain
, isl_dim_param
);
2128 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2130 isl_space_free(domain
);
2134 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
2135 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
2138 struct isl_upoly_rec
*rec
;
2139 struct isl_upoly
*base
, *res
;
2144 if (isl_upoly_is_cst(up
))
2147 if (up
->var
< first
)
2150 rec
= isl_upoly_as_rec(up
);
2154 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2156 if (up
->var
>= first
+ n
)
2157 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
2159 base
= isl_upoly_copy(subs
[up
->var
- first
]);
2161 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2162 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2163 struct isl_upoly
*t
;
2164 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
2165 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2166 res
= isl_upoly_sum(res
, t
);
2169 isl_upoly_free(base
);
2178 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2179 isl_int denom
, unsigned len
)
2182 struct isl_upoly
*up
;
2184 isl_assert(ctx
, len
>= 1, return NULL
);
2186 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2187 for (i
= 0; i
< len
- 1; ++i
) {
2188 struct isl_upoly
*t
;
2189 struct isl_upoly
*c
;
2191 if (isl_int_is_zero(f
[1 + i
]))
2194 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2195 t
= isl_upoly_var_pow(ctx
, i
, 1);
2196 t
= isl_upoly_mul(c
, t
);
2197 up
= isl_upoly_sum(up
, t
);
2203 /* Remove common factor of non-constant terms and denominator.
2205 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2207 isl_ctx
*ctx
= qp
->div
->ctx
;
2208 unsigned total
= qp
->div
->n_col
- 2;
2210 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2211 isl_int_gcd(ctx
->normalize_gcd
,
2212 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2213 if (isl_int_is_one(ctx
->normalize_gcd
))
2216 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2217 ctx
->normalize_gcd
, total
);
2218 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2219 ctx
->normalize_gcd
);
2220 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2221 ctx
->normalize_gcd
);
2224 /* Replace the integer division identified by "div" by the polynomial "s".
2225 * The integer division is assumed not to appear in the definition
2226 * of any other integer divisions.
2228 static __isl_give isl_qpolynomial
*substitute_div(
2229 __isl_take isl_qpolynomial
*qp
,
2230 int div
, __isl_take
struct isl_upoly
*s
)
2239 qp
= isl_qpolynomial_cow(qp
);
2243 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2244 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2248 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2251 for (i
= 0; i
< total
+ div
; ++i
)
2253 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2254 reordering
[i
] = i
- 1;
2255 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2256 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2257 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2260 if (!qp
->upoly
|| !qp
->div
)
2266 isl_qpolynomial_free(qp
);
2271 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2272 * divisions because d is equal to 1 by their definition, i.e., e.
2274 static __isl_give isl_qpolynomial
*substitute_non_divs(
2275 __isl_take isl_qpolynomial
*qp
)
2279 struct isl_upoly
*s
;
2284 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2285 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2286 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2288 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2289 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2291 isl_seq_combine(qp
->div
->row
[j
] + 1,
2292 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2293 qp
->div
->row
[j
][2 + total
+ i
],
2294 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2295 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2296 normalize_div(qp
, j
);
2298 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2299 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2300 qp
= substitute_div(qp
, i
, s
);
2307 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2308 * with d the denominator. When replacing the coefficient e of x by
2309 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2310 * inside the division, so we need to add floor(e/d) * x outside.
2311 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2312 * to adjust the coefficient of x in each later div that depends on the
2313 * current div "div" and also in the affine expressions in the rows of "mat"
2314 * (if they too depend on "div").
2316 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2317 __isl_keep isl_mat
**mat
)
2321 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2324 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2325 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2326 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2328 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2329 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2330 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2331 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2332 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2333 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2335 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2336 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2342 /* Check if the last non-zero coefficient is bigger that half of the
2343 * denominator. If so, we will invert the div to further reduce the number
2344 * of distinct divs that may appear.
2345 * If the last non-zero coefficient is exactly half the denominator,
2346 * then we continue looking for earlier coefficients that are bigger
2347 * than half the denominator.
2349 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2354 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2355 if (isl_int_is_zero(div
->row
[row
][i
]))
2357 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2358 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2359 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2369 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2370 * We only invert the coefficients of e (and the coefficient of q in
2371 * later divs and in the rows of "mat"). After calling this function, the
2372 * coefficients of e should be reduced again.
2374 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2375 __isl_keep isl_mat
**mat
)
2377 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2379 isl_seq_neg(qp
->div
->row
[div
] + 1,
2380 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2381 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2382 isl_int_add(qp
->div
->row
[div
][1],
2383 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2384 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2385 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2386 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2389 /* Reduce all divs of "qp" to have coefficients
2390 * in the interval [0, d-1], with d the denominator and such that the
2391 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2392 * The modifications to the integer divisions need to be reflected
2393 * in the factors of the polynomial that refer to the original
2394 * integer divisions. To this end, the modifications are collected
2395 * as a set of affine expressions and then plugged into the polynomial.
2397 * After the reduction, some divs may have become redundant or identical,
2398 * so we call substitute_non_divs and sort_divs. If these functions
2399 * eliminate divs or merge two or more divs into one, the coefficients
2400 * of the enclosing divs may have to be reduced again, so we call
2401 * ourselves recursively if the number of divs decreases.
2403 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2408 struct isl_upoly
**s
;
2409 unsigned o_div
, n_div
, total
;
2414 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2415 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2416 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2417 ctx
= isl_qpolynomial_get_ctx(qp
);
2418 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2420 for (i
= 0; i
< n_div
; ++i
)
2421 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2423 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2424 normalize_div(qp
, i
);
2425 reduce_div(qp
, i
, &mat
);
2426 if (needs_invert(qp
->div
, i
)) {
2427 invert_div(qp
, i
, &mat
);
2428 reduce_div(qp
, i
, &mat
);
2434 s
= isl_alloc_array(ctx
, struct isl_upoly
*, n_div
);
2437 for (i
= 0; i
< n_div
; ++i
)
2438 s
[i
] = isl_upoly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2440 qp
->upoly
= isl_upoly_subs(qp
->upoly
, o_div
- 1, n_div
, s
);
2441 for (i
= 0; i
< n_div
; ++i
)
2442 isl_upoly_free(s
[i
]);
2449 qp
= substitute_non_divs(qp
);
2451 if (qp
&& isl_qpolynomial_domain_dim(qp
, isl_dim_div
) < n_div
)
2452 return reduce_divs(qp
);
2456 isl_qpolynomial_free(qp
);
2461 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2462 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2464 struct isl_qpolynomial
*qp
;
2465 struct isl_upoly_cst
*cst
;
2467 qp
= isl_qpolynomial_zero_on_domain(domain
);
2471 cst
= isl_upoly_as_cst(qp
->upoly
);
2472 isl_int_set(cst
->n
, n
);
2473 isl_int_set(cst
->d
, d
);
2478 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2480 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2481 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2483 isl_qpolynomial
*qp
;
2484 struct isl_upoly_cst
*cst
;
2486 qp
= isl_qpolynomial_zero_on_domain(domain
);
2490 cst
= isl_upoly_as_cst(qp
->upoly
);
2491 isl_int_set(cst
->n
, val
->n
);
2492 isl_int_set(cst
->d
, val
->d
);
2498 isl_qpolynomial_free(qp
);
2502 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2504 struct isl_upoly_rec
*rec
;
2510 if (isl_upoly_is_cst(up
))
2514 active
[up
->var
] = 1;
2516 rec
= isl_upoly_as_rec(up
);
2517 for (i
= 0; i
< rec
->n
; ++i
)
2518 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2524 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2527 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2532 for (i
= 0; i
< d
; ++i
)
2533 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2534 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2540 return up_set_active(qp
->upoly
, active
, d
);
2543 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2544 enum isl_dim_type type
, unsigned first
, unsigned n
)
2548 isl_bool involves
= isl_bool_false
;
2551 return isl_bool_error
;
2553 return isl_bool_false
;
2555 isl_assert(qp
->dim
->ctx
,
2556 first
+ n
<= isl_qpolynomial_dim(qp
, type
),
2557 return isl_bool_error
);
2558 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2559 type
== isl_dim_in
, return isl_bool_error
);
2561 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2562 isl_space_dim(qp
->dim
, isl_dim_all
));
2563 if (set_active(qp
, active
) < 0)
2566 if (type
== isl_dim_in
)
2567 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2568 for (i
= 0; i
< n
; ++i
)
2569 if (active
[first
+ i
]) {
2570 involves
= isl_bool_true
;
2579 return isl_bool_error
;
2582 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2583 * of the divs that do appear in the quasi-polynomial.
2585 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2586 __isl_take isl_qpolynomial
*qp
)
2593 int *reordering
= NULL
;
2600 if (qp
->div
->n_row
== 0)
2603 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2604 len
= qp
->div
->n_col
- 2;
2605 ctx
= isl_qpolynomial_get_ctx(qp
);
2606 active
= isl_calloc_array(ctx
, int, len
);
2610 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2613 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2614 if (!active
[d
+ i
]) {
2618 for (j
= 0; j
< i
; ++j
) {
2619 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2631 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2635 for (i
= 0; i
< d
; ++i
)
2639 n_div
= qp
->div
->n_row
;
2640 for (i
= 0; i
< n_div
; ++i
) {
2641 if (!active
[d
+ i
]) {
2642 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2643 qp
->div
= isl_mat_drop_cols(qp
->div
,
2644 2 + d
+ i
- skip
, 1);
2647 reordering
[d
+ i
] = d
+ i
- skip
;
2650 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2652 if (!qp
->upoly
|| !qp
->div
)
2662 isl_qpolynomial_free(qp
);
2666 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2667 unsigned first
, unsigned n
)
2670 struct isl_upoly_rec
*rec
;
2674 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2676 if (up
->var
< first
+ n
) {
2677 up
= replace_by_constant_term(up
);
2678 return isl_upoly_drop(up
, first
, n
);
2680 up
= isl_upoly_cow(up
);
2684 rec
= isl_upoly_as_rec(up
);
2688 for (i
= 0; i
< rec
->n
; ++i
) {
2689 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2700 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2701 __isl_take isl_qpolynomial
*qp
,
2702 enum isl_dim_type type
, unsigned pos
, const char *s
)
2704 qp
= isl_qpolynomial_cow(qp
);
2707 if (type
== isl_dim_out
)
2708 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2709 "cannot set name of output/set dimension",
2710 return isl_qpolynomial_free(qp
));
2711 type
= domain_type(type
);
2712 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2717 isl_qpolynomial_free(qp
);
2721 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2722 __isl_take isl_qpolynomial
*qp
,
2723 enum isl_dim_type type
, unsigned first
, unsigned n
)
2727 if (type
== isl_dim_out
)
2728 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2729 "cannot drop output/set dimension",
2731 type
= domain_type(type
);
2732 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2735 qp
= isl_qpolynomial_cow(qp
);
2739 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2741 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2742 type
== isl_dim_set
, goto error
);
2744 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2748 if (type
== isl_dim_set
)
2749 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2751 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2755 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2761 isl_qpolynomial_free(qp
);
2765 /* Project the domain of the quasi-polynomial onto its parameter space.
2766 * The quasi-polynomial may not involve any of the domain dimensions.
2768 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2769 __isl_take isl_qpolynomial
*qp
)
2775 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2776 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2778 return isl_qpolynomial_free(qp
);
2780 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2781 "polynomial involves some of the domain dimensions",
2782 return isl_qpolynomial_free(qp
));
2783 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2784 space
= isl_qpolynomial_get_domain_space(qp
);
2785 space
= isl_space_params(space
);
2786 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2790 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2791 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2797 struct isl_upoly
*up
;
2801 if (eq
->n_eq
== 0) {
2802 isl_basic_set_free(eq
);
2806 qp
= isl_qpolynomial_cow(qp
);
2809 qp
->div
= isl_mat_cow(qp
->div
);
2813 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2815 isl_int_init(denom
);
2816 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2817 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2818 if (j
< 0 || j
== 0 || j
>= total
)
2821 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2822 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2824 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2825 &qp
->div
->row
[k
][0]);
2826 normalize_div(qp
, k
);
2829 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2830 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2831 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2832 isl_int_set_si(eq
->eq
[i
][j
], 0);
2834 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2835 eq
->eq
[i
], denom
, total
);
2836 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2839 isl_int_clear(denom
);
2844 isl_basic_set_free(eq
);
2846 qp
= substitute_non_divs(qp
);
2851 isl_basic_set_free(eq
);
2852 isl_qpolynomial_free(qp
);
2856 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2858 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2859 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2863 if (qp
->div
->n_row
> 0)
2864 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2865 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2867 isl_basic_set_free(eq
);
2868 isl_qpolynomial_free(qp
);
2872 /* Look for equalities among the variables shared by context and qp
2873 * and the integer divisions of qp, if any.
2874 * The equalities are then used to eliminate variables and/or integer
2875 * divisions from qp.
2877 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2878 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2880 isl_local_space
*ls
;
2883 ls
= isl_qpolynomial_get_domain_local_space(qp
);
2884 context
= isl_local_space_lift_set(ls
, context
);
2886 aff
= isl_set_affine_hull(context
);
2887 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2890 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2891 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2893 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2894 isl_set
*dom_context
= isl_set_universe(space
);
2895 dom_context
= isl_set_intersect_params(dom_context
, context
);
2896 return isl_qpolynomial_gist(qp
, dom_context
);
2899 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2900 __isl_take isl_qpolynomial
*qp
)
2906 if (isl_qpolynomial_is_zero(qp
)) {
2907 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2908 isl_qpolynomial_free(qp
);
2909 return isl_pw_qpolynomial_zero(dim
);
2912 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2913 return isl_pw_qpolynomial_alloc(dom
, qp
);
2916 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
2919 #define PW isl_pw_qpolynomial
2921 #define EL isl_qpolynomial
2923 #define EL_IS_ZERO is_zero
2927 #define IS_ZERO is_zero
2930 #undef DEFAULT_IS_ZERO
2931 #define DEFAULT_IS_ZERO 1
2935 #include <isl_pw_templ.c>
2936 #include <isl_pw_eval.c>
2939 #define BASE pw_qpolynomial
2941 #include <isl_union_single.c>
2942 #include <isl_union_eval.c>
2943 #include <isl_union_neg.c>
2945 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2953 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2956 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2959 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2960 __isl_take isl_pw_qpolynomial
*pwqp1
,
2961 __isl_take isl_pw_qpolynomial
*pwqp2
)
2963 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2966 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2967 __isl_take isl_pw_qpolynomial
*pwqp1
,
2968 __isl_take isl_pw_qpolynomial
*pwqp2
)
2971 struct isl_pw_qpolynomial
*res
;
2973 if (!pwqp1
|| !pwqp2
)
2976 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2979 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2980 isl_pw_qpolynomial_free(pwqp2
);
2984 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2985 isl_pw_qpolynomial_free(pwqp1
);
2989 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2990 isl_pw_qpolynomial_free(pwqp1
);
2994 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2995 isl_pw_qpolynomial_free(pwqp2
);
2999 n
= pwqp1
->n
* pwqp2
->n
;
3000 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3002 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3003 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3004 struct isl_set
*common
;
3005 struct isl_qpolynomial
*prod
;
3006 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3007 isl_set_copy(pwqp2
->p
[j
].set
));
3008 if (isl_set_plain_is_empty(common
)) {
3009 isl_set_free(common
);
3013 prod
= isl_qpolynomial_mul(
3014 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3015 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3017 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3021 isl_pw_qpolynomial_free(pwqp1
);
3022 isl_pw_qpolynomial_free(pwqp2
);
3026 isl_pw_qpolynomial_free(pwqp1
);
3027 isl_pw_qpolynomial_free(pwqp2
);
3031 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
3032 __isl_take isl_vec
*vec
)
3035 struct isl_upoly_rec
*rec
;
3039 if (isl_upoly_is_cst(up
)) {
3041 res
= isl_upoly_get_constant_val(up
);
3046 rec
= isl_upoly_as_rec(up
);
3050 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
3052 base
= isl_val_rat_from_isl_int(up
->ctx
,
3053 vec
->el
[1 + up
->var
], vec
->el
[0]);
3055 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
3058 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3059 res
= isl_val_mul(res
, isl_val_copy(base
));
3060 res
= isl_val_add(res
,
3061 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
3062 isl_vec_copy(vec
)));
3075 /* Evaluate "qp" in the void point "pnt".
3076 * In particular, return the value NaN.
3078 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3079 __isl_take isl_point
*pnt
)
3083 ctx
= isl_point_get_ctx(pnt
);
3084 isl_qpolynomial_free(qp
);
3085 isl_point_free(pnt
);
3086 return isl_val_nan(ctx
);
3089 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3090 __isl_take isl_point
*pnt
)
3098 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3099 is_void
= isl_point_is_void(pnt
);
3103 return eval_void(qp
, pnt
);
3105 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3107 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
3109 isl_qpolynomial_free(qp
);
3110 isl_point_free(pnt
);
3114 isl_qpolynomial_free(qp
);
3115 isl_point_free(pnt
);
3119 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
3120 __isl_keep
struct isl_upoly_cst
*cst2
)
3125 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3126 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3127 cmp
= isl_int_sgn(t
);
3132 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3133 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3134 unsigned first
, unsigned n
)
3142 if (type
== isl_dim_out
)
3143 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3144 "cannot insert output/set dimensions",
3146 type
= domain_type(type
);
3147 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3150 qp
= isl_qpolynomial_cow(qp
);
3154 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3157 g_pos
= pos(qp
->dim
, type
) + first
;
3159 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3163 total
= qp
->div
->n_col
- 2;
3164 if (total
> g_pos
) {
3166 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3169 for (i
= 0; i
< total
- g_pos
; ++i
)
3171 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3177 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3183 isl_qpolynomial_free(qp
);
3187 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3188 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3192 pos
= isl_qpolynomial_dim(qp
, type
);
3194 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3197 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3198 __isl_take isl_pw_qpolynomial
*pwqp
,
3199 enum isl_dim_type type
, unsigned n
)
3203 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3205 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3208 static int *reordering_move(isl_ctx
*ctx
,
3209 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3214 reordering
= isl_alloc_array(ctx
, int, len
);
3219 for (i
= 0; i
< dst
; ++i
)
3221 for (i
= 0; i
< n
; ++i
)
3222 reordering
[src
+ i
] = dst
+ i
;
3223 for (i
= 0; i
< src
- dst
; ++i
)
3224 reordering
[dst
+ i
] = dst
+ n
+ i
;
3225 for (i
= 0; i
< len
- src
- n
; ++i
)
3226 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3228 for (i
= 0; i
< src
; ++i
)
3230 for (i
= 0; i
< n
; ++i
)
3231 reordering
[src
+ i
] = dst
+ i
;
3232 for (i
= 0; i
< dst
- src
; ++i
)
3233 reordering
[src
+ n
+ i
] = src
+ i
;
3234 for (i
= 0; i
< len
- dst
- n
; ++i
)
3235 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3241 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3242 __isl_take isl_qpolynomial
*qp
,
3243 enum isl_dim_type dst_type
, unsigned dst_pos
,
3244 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3253 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3254 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3255 "cannot move output/set dimension",
3257 if (dst_type
== isl_dim_in
)
3258 dst_type
= isl_dim_set
;
3259 if (src_type
== isl_dim_in
)
3260 src_type
= isl_dim_set
;
3263 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3264 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3267 qp
= isl_qpolynomial_cow(qp
);
3271 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3274 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3275 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3276 if (dst_type
> src_type
)
3279 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3286 reordering
= reordering_move(qp
->dim
->ctx
,
3287 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3291 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3296 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3302 isl_qpolynomial_free(qp
);
3306 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3307 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3309 struct isl_upoly
*up
;
3311 space
= isl_space_domain(space
);
3315 up
= isl_upoly_from_affine(space
->ctx
, f
, denom
,
3316 1 + isl_space_dim(space
, isl_dim_all
));
3318 return isl_qpolynomial_alloc(space
, 0, up
);
3321 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3324 struct isl_upoly
*up
;
3325 isl_qpolynomial
*qp
;
3330 ctx
= isl_aff_get_ctx(aff
);
3331 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3334 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3335 aff
->ls
->div
->n_row
, up
);
3339 isl_mat_free(qp
->div
);
3340 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3341 qp
->div
= isl_mat_cow(qp
->div
);
3346 qp
= reduce_divs(qp
);
3347 qp
= remove_redundant_divs(qp
);
3351 return isl_qpolynomial_free(qp
);
3354 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3355 __isl_take isl_pw_aff
*pwaff
)
3358 isl_pw_qpolynomial
*pwqp
;
3363 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3366 for (i
= 0; i
< pwaff
->n
; ++i
) {
3368 isl_qpolynomial
*qp
;
3370 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3371 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3372 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3375 isl_pw_aff_free(pwaff
);
3379 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3380 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3384 aff
= isl_constraint_get_bound(c
, type
, pos
);
3385 isl_constraint_free(c
);
3386 return isl_qpolynomial_from_aff(aff
);
3389 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3390 * in "qp" by subs[i].
3392 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3393 __isl_take isl_qpolynomial
*qp
,
3394 enum isl_dim_type type
, unsigned first
, unsigned n
,
3395 __isl_keep isl_qpolynomial
**subs
)
3398 struct isl_upoly
**ups
;
3403 qp
= isl_qpolynomial_cow(qp
);
3407 if (type
== isl_dim_out
)
3408 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3409 "cannot substitute output/set dimension",
3411 type
= domain_type(type
);
3413 for (i
= 0; i
< n
; ++i
)
3417 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3420 for (i
= 0; i
< n
; ++i
)
3421 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3424 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3425 for (i
= 0; i
< n
; ++i
)
3426 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3428 first
+= pos(qp
->dim
, type
);
3430 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3433 for (i
= 0; i
< n
; ++i
)
3434 ups
[i
] = subs
[i
]->upoly
;
3436 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3445 isl_qpolynomial_free(qp
);
3449 /* Extend "bset" with extra set dimensions for each integer division
3450 * in "qp" and then call "fn" with the extended bset and the polynomial
3451 * that results from replacing each of the integer divisions by the
3452 * corresponding extra set dimension.
3454 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3455 __isl_keep isl_basic_set
*bset
,
3456 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3457 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3460 isl_local_space
*ls
;
3461 isl_qpolynomial
*poly
;
3464 return isl_stat_error
;
3465 if (qp
->div
->n_row
== 0)
3466 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3469 space
= isl_space_copy(qp
->dim
);
3470 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3471 poly
= isl_qpolynomial_alloc(space
, 0, isl_upoly_copy(qp
->upoly
));
3472 bset
= isl_basic_set_copy(bset
);
3473 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3474 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3476 return fn(bset
, poly
, user
);
3479 /* Return total degree in variables first (inclusive) up to last (exclusive).
3481 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3485 struct isl_upoly_rec
*rec
;
3489 if (isl_upoly_is_zero(up
))
3491 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3494 rec
= isl_upoly_as_rec(up
);
3498 for (i
= 0; i
< rec
->n
; ++i
) {
3501 if (isl_upoly_is_zero(rec
->p
[i
]))
3503 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3513 /* Return total degree in set variables.
3515 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3523 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3524 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3525 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3528 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3529 unsigned pos
, int deg
)
3532 struct isl_upoly_rec
*rec
;
3537 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3539 return isl_upoly_copy(up
);
3541 return isl_upoly_zero(up
->ctx
);
3544 rec
= isl_upoly_as_rec(up
);
3548 if (up
->var
== pos
) {
3550 return isl_upoly_copy(rec
->p
[deg
]);
3552 return isl_upoly_zero(up
->ctx
);
3555 up
= isl_upoly_copy(up
);
3556 up
= isl_upoly_cow(up
);
3557 rec
= isl_upoly_as_rec(up
);
3561 for (i
= 0; i
< rec
->n
; ++i
) {
3562 struct isl_upoly
*t
;
3563 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3566 isl_upoly_free(rec
->p
[i
]);
3576 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3578 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3579 __isl_keep isl_qpolynomial
*qp
,
3580 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3583 struct isl_upoly
*up
;
3589 if (type
== isl_dim_out
)
3590 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3591 "output/set dimension does not have a coefficient",
3593 type
= domain_type(type
);
3595 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3598 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3599 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3601 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3604 isl_mat_free(c
->div
);
3605 c
->div
= isl_mat_copy(qp
->div
);
3610 isl_qpolynomial_free(c
);
3614 /* Homogenize the polynomial in the variables first (inclusive) up to
3615 * last (exclusive) by inserting powers of variable first.
3616 * Variable first is assumed not to appear in the input.
3618 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3619 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3620 int first
, int last
)
3623 struct isl_upoly_rec
*rec
;
3627 if (isl_upoly_is_zero(up
))
3631 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3632 struct isl_upoly
*hom
;
3634 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3637 rec
= isl_upoly_as_rec(hom
);
3638 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3643 up
= isl_upoly_cow(up
);
3644 rec
= isl_upoly_as_rec(up
);
3648 for (i
= 0; i
< rec
->n
; ++i
) {
3649 if (isl_upoly_is_zero(rec
->p
[i
]))
3651 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3652 up
->var
< last
? deg
+ i
: i
, target
,
3664 /* Homogenize the polynomial in the set variables by introducing
3665 * powers of an extra set variable at position 0.
3667 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3668 __isl_take isl_qpolynomial
*poly
)
3672 int deg
= isl_qpolynomial_degree(poly
);
3677 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3678 poly
= isl_qpolynomial_cow(poly
);
3682 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3683 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3684 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3691 isl_qpolynomial_free(poly
);
3695 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3696 __isl_take isl_mat
*div
)
3704 n
= isl_space_dim(space
, isl_dim_all
) + div
->n_row
;
3706 term
= isl_calloc(space
->ctx
, struct isl_term
,
3707 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3714 isl_int_init(term
->n
);
3715 isl_int_init(term
->d
);
3719 isl_space_free(space
);
3724 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3733 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3742 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3744 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3748 isl_int_set(dup
->n
, term
->n
);
3749 isl_int_set(dup
->d
, term
->d
);
3751 for (i
= 0; i
< total
; ++i
)
3752 dup
->pow
[i
] = term
->pow
[i
];
3757 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3765 return isl_term_dup(term
);
3768 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3773 if (--term
->ref
> 0)
3776 isl_space_free(term
->dim
);
3777 isl_mat_free(term
->div
);
3778 isl_int_clear(term
->n
);
3779 isl_int_clear(term
->d
);
3785 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3793 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3794 case isl_dim_div
: return term
->div
->n_row
;
3795 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3801 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3803 return term
? term
->dim
->ctx
: NULL
;
3806 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3810 isl_int_set(*n
, term
->n
);
3813 /* Return the coefficient of the term "term".
3815 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3820 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3824 int isl_term_get_exp(__isl_keep isl_term
*term
,
3825 enum isl_dim_type type
, unsigned pos
)
3830 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3832 if (type
>= isl_dim_set
)
3833 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3834 if (type
>= isl_dim_div
)
3835 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3837 return term
->pow
[pos
];
3840 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3842 isl_local_space
*ls
;
3848 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3851 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3852 isl_mat_copy(term
->div
));
3853 aff
= isl_aff_alloc(ls
);
3857 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3859 aff
= isl_aff_normalize(aff
);
3864 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3865 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3866 __isl_take isl_term
*term
, void *user
)
3869 struct isl_upoly_rec
*rec
;
3874 if (isl_upoly_is_zero(up
))
3877 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3878 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3879 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3881 if (isl_upoly_is_cst(up
)) {
3882 struct isl_upoly_cst
*cst
;
3883 cst
= isl_upoly_as_cst(up
);
3886 term
= isl_term_cow(term
);
3889 isl_int_set(term
->n
, cst
->n
);
3890 isl_int_set(term
->d
, cst
->d
);
3891 if (fn(isl_term_copy(term
), user
) < 0)
3896 rec
= isl_upoly_as_rec(up
);
3900 for (i
= 0; i
< rec
->n
; ++i
) {
3901 term
= isl_term_cow(term
);
3904 term
->pow
[up
->var
] = i
;
3905 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3909 term
->pow
[up
->var
] = 0;
3913 isl_term_free(term
);
3917 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3918 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3923 return isl_stat_error
;
3925 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3927 return isl_stat_error
;
3929 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3931 isl_term_free(term
);
3933 return term
? isl_stat_ok
: isl_stat_error
;
3936 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3938 struct isl_upoly
*up
;
3939 isl_qpolynomial
*qp
;
3945 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3947 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3948 for (i
= 0; i
< n
; ++i
) {
3951 up
= isl_upoly_mul(up
,
3952 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3955 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3958 isl_mat_free(qp
->div
);
3959 qp
->div
= isl_mat_copy(term
->div
);
3963 isl_term_free(term
);
3966 isl_qpolynomial_free(qp
);
3967 isl_term_free(term
);
3971 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3972 __isl_take isl_space
*space
)
3981 if (isl_space_is_equal(qp
->dim
, space
)) {
3982 isl_space_free(space
);
3986 qp
= isl_qpolynomial_cow(qp
);
3990 extra
= isl_space_dim(space
, isl_dim_set
) -
3991 isl_space_dim(qp
->dim
, isl_dim_set
);
3992 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3993 if (qp
->div
->n_row
) {
3996 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3999 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4001 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
4006 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4009 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4010 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4012 isl_space_free(qp
->dim
);
4017 isl_space_free(space
);
4018 isl_qpolynomial_free(qp
);
4022 /* For each parameter or variable that does not appear in qp,
4023 * first eliminate the variable from all constraints and then set it to zero.
4025 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4026 __isl_keep isl_qpolynomial
*qp
)
4037 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4038 active
= isl_calloc_array(set
->ctx
, int, d
);
4039 if (set_active(qp
, active
) < 0)
4042 for (i
= 0; i
< d
; ++i
)
4051 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4052 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4053 for (i
= 0; i
< nparam
; ++i
) {
4056 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4057 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4059 for (i
= 0; i
< nvar
; ++i
) {
4060 if (active
[nparam
+ i
])
4062 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4063 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4075 struct isl_opt_data
{
4076 isl_qpolynomial
*qp
;
4082 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4084 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4087 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4091 } else if (data
->max
) {
4092 data
->opt
= isl_val_max(data
->opt
, val
);
4094 data
->opt
= isl_val_min(data
->opt
, val
);
4100 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4101 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4103 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4108 if (isl_upoly_is_cst(qp
->upoly
)) {
4110 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4111 isl_qpolynomial_free(qp
);
4115 set
= fix_inactive(set
, qp
);
4118 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4122 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4125 isl_qpolynomial_free(qp
);
4129 isl_qpolynomial_free(qp
);
4130 isl_val_free(data
.opt
);
4134 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4135 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4140 struct isl_upoly
**subs
;
4141 isl_mat
*mat
, *diag
;
4143 qp
= isl_qpolynomial_cow(qp
);
4148 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4150 n_sub
= morph
->inv
->n_row
- 1;
4151 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4152 n_sub
+= qp
->div
->n_row
;
4153 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4157 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4158 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4159 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4160 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4161 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4162 subs
[morph
->inv
->n_row
- 1 + i
] =
4163 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4165 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4167 for (i
= 0; i
< n_sub
; ++i
)
4168 isl_upoly_free(subs
[i
]);
4171 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4172 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4173 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4174 mat
= isl_mat_diagonal(mat
, diag
);
4175 qp
->div
= isl_mat_product(qp
->div
, mat
);
4176 isl_space_free(qp
->dim
);
4177 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4179 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4182 isl_morph_free(morph
);
4186 isl_qpolynomial_free(qp
);
4187 isl_morph_free(morph
);
4191 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4192 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4193 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4195 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4196 &isl_pw_qpolynomial_mul
);
4199 /* Reorder the dimension of "qp" according to the given reordering.
4201 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4202 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4206 qp
= isl_qpolynomial_cow(qp
);
4210 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4214 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4218 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4222 space
= isl_reordering_get_space(r
);
4223 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4225 isl_reordering_free(r
);
4228 isl_qpolynomial_free(qp
);
4229 isl_reordering_free(r
);
4233 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4234 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4236 isl_bool equal_params
;
4241 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4242 if (equal_params
< 0)
4244 if (!equal_params
) {
4245 isl_reordering
*exp
;
4247 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4248 exp
= isl_reordering_extend_space(exp
,
4249 isl_qpolynomial_get_domain_space(qp
));
4250 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4253 isl_space_free(model
);
4256 isl_space_free(model
);
4257 isl_qpolynomial_free(qp
);
4261 struct isl_split_periods_data
{
4263 isl_pw_qpolynomial
*res
;
4266 /* Create a slice where the integer division "div" has the fixed value "v".
4267 * In particular, if "div" refers to floor(f/m), then create a slice
4269 * m v <= f <= m v + (m - 1)
4274 * -f + m v + (m - 1) >= 0
4276 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4277 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4280 isl_basic_set
*bset
= NULL
;
4286 total
= isl_space_dim(space
, isl_dim_all
);
4287 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4289 k
= isl_basic_set_alloc_inequality(bset
);
4292 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4293 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4295 k
= isl_basic_set_alloc_inequality(bset
);
4298 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4299 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4300 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4301 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4303 isl_space_free(space
);
4304 return isl_set_from_basic_set(bset
);
4306 isl_basic_set_free(bset
);
4307 isl_space_free(space
);
4311 static isl_stat
split_periods(__isl_take isl_set
*set
,
4312 __isl_take isl_qpolynomial
*qp
, void *user
);
4314 /* Create a slice of the domain "set" such that integer division "div"
4315 * has the fixed value "v" and add the results to data->res,
4316 * replacing the integer division by "v" in "qp".
4318 static isl_stat
set_div(__isl_take isl_set
*set
,
4319 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4320 struct isl_split_periods_data
*data
)
4325 struct isl_upoly
*cst
;
4327 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4328 set
= isl_set_intersect(set
, slice
);
4333 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4335 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4336 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4338 isl_int_addmul(qp
->div
->row
[i
][1],
4339 qp
->div
->row
[i
][2 + total
+ div
], v
);
4340 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4343 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4344 qp
= substitute_div(qp
, div
, cst
);
4346 return split_periods(set
, qp
, data
);
4349 isl_qpolynomial_free(qp
);
4350 return isl_stat_error
;
4353 /* Split the domain "set" such that integer division "div"
4354 * has a fixed value (ranging from "min" to "max") on each slice
4355 * and add the results to data->res.
4357 static isl_stat
split_div(__isl_take isl_set
*set
,
4358 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4359 struct isl_split_periods_data
*data
)
4361 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4362 isl_set
*set_i
= isl_set_copy(set
);
4363 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4365 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4369 isl_qpolynomial_free(qp
);
4373 isl_qpolynomial_free(qp
);
4374 return isl_stat_error
;
4377 /* If "qp" refers to any integer division
4378 * that can only attain "max_periods" distinct values on "set"
4379 * then split the domain along those distinct values.
4380 * Add the results (or the original if no splitting occurs)
4383 static isl_stat
split_periods(__isl_take isl_set
*set
,
4384 __isl_take isl_qpolynomial
*qp
, void *user
)
4387 isl_pw_qpolynomial
*pwqp
;
4388 struct isl_split_periods_data
*data
;
4391 isl_stat r
= isl_stat_ok
;
4393 data
= (struct isl_split_periods_data
*)user
;
4398 if (qp
->div
->n_row
== 0) {
4399 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4400 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4406 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4407 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4408 enum isl_lp_result lp_res
;
4410 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4411 qp
->div
->n_row
) != -1)
4414 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4415 set
->ctx
->one
, &min
, NULL
, NULL
);
4416 if (lp_res
== isl_lp_error
)
4418 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4420 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4422 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4423 set
->ctx
->one
, &max
, NULL
, NULL
);
4424 if (lp_res
== isl_lp_error
)
4426 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4428 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4430 isl_int_sub(max
, max
, min
);
4431 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4432 isl_int_add(max
, max
, min
);
4437 if (i
< qp
->div
->n_row
) {
4438 r
= split_div(set
, qp
, i
, min
, max
, data
);
4440 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4441 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4453 isl_qpolynomial_free(qp
);
4454 return isl_stat_error
;
4457 /* If any quasi-polynomial in pwqp refers to any integer division
4458 * that can only attain "max_periods" distinct values on its domain
4459 * then split the domain along those distinct values.
4461 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4462 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4464 struct isl_split_periods_data data
;
4466 data
.max_periods
= max_periods
;
4467 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4469 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4472 isl_pw_qpolynomial_free(pwqp
);
4476 isl_pw_qpolynomial_free(data
.res
);
4477 isl_pw_qpolynomial_free(pwqp
);
4481 /* Construct a piecewise quasipolynomial that is constant on the given
4482 * domain. In particular, it is
4485 * infinity if cst == -1
4487 * If cst == -1, then explicitly check whether the domain is empty and,
4488 * if so, return 0 instead.
4490 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4491 __isl_take isl_basic_set
*bset
, int cst
)
4494 isl_qpolynomial
*qp
;
4496 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4501 bset
= isl_basic_set_params(bset
);
4502 dim
= isl_basic_set_get_space(bset
);
4504 qp
= isl_qpolynomial_infty_on_domain(dim
);
4506 qp
= isl_qpolynomial_zero_on_domain(dim
);
4508 qp
= isl_qpolynomial_one_on_domain(dim
);
4509 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4512 /* Factor bset, call fn on each of the factors and return the product.
4514 * If no factors can be found, simply call fn on the input.
4515 * Otherwise, construct the factors based on the factorizer,
4516 * call fn on each factor and compute the product.
4518 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4519 __isl_take isl_basic_set
*bset
,
4520 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4526 isl_qpolynomial
*qp
;
4527 isl_pw_qpolynomial
*pwqp
;
4531 f
= isl_basic_set_factorizer(bset
);
4534 if (f
->n_group
== 0) {
4535 isl_factorizer_free(f
);
4539 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4540 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4542 space
= isl_basic_set_get_space(bset
);
4543 space
= isl_space_params(space
);
4544 set
= isl_set_universe(isl_space_copy(space
));
4545 qp
= isl_qpolynomial_one_on_domain(space
);
4546 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4548 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4550 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4551 isl_basic_set
*bset_i
;
4552 isl_pw_qpolynomial
*pwqp_i
;
4554 bset_i
= isl_basic_set_copy(bset
);
4555 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4556 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4557 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4559 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4560 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4561 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4563 pwqp_i
= fn(bset_i
);
4564 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4569 isl_basic_set_free(bset
);
4570 isl_factorizer_free(f
);
4574 isl_basic_set_free(bset
);
4578 /* Factor bset, call fn on each of the factors and return the product.
4579 * The function is assumed to evaluate to zero on empty domains,
4580 * to one on zero-dimensional domains and to infinity on unbounded domains
4581 * and will not be called explicitly on zero-dimensional or unbounded domains.
4583 * We first check for some special cases and remove all equalities.
4584 * Then we hand over control to compressed_multiplicative_call.
4586 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4587 __isl_take isl_basic_set
*bset
,
4588 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4592 isl_pw_qpolynomial
*pwqp
;
4597 if (isl_basic_set_plain_is_empty(bset
))
4598 return constant_on_domain(bset
, 0);
4600 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4601 return constant_on_domain(bset
, 1);
4603 bounded
= isl_basic_set_is_bounded(bset
);
4607 return constant_on_domain(bset
, -1);
4609 if (bset
->n_eq
== 0)
4610 return compressed_multiplicative_call(bset
, fn
);
4612 morph
= isl_basic_set_full_compression(bset
);
4613 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4615 pwqp
= compressed_multiplicative_call(bset
, fn
);
4617 morph
= isl_morph_dom_params(morph
);
4618 morph
= isl_morph_ran_params(morph
);
4619 morph
= isl_morph_inverse(morph
);
4621 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4625 isl_basic_set_free(bset
);
4629 /* Drop all floors in "qp", turning each integer division [a/m] into
4630 * a rational division a/m. If "down" is set, then the integer division
4631 * is replaced by (a-(m-1))/m instead.
4633 static __isl_give isl_qpolynomial
*qp_drop_floors(
4634 __isl_take isl_qpolynomial
*qp
, int down
)
4637 struct isl_upoly
*s
;
4641 if (qp
->div
->n_row
== 0)
4644 qp
= isl_qpolynomial_cow(qp
);
4648 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4650 isl_int_sub(qp
->div
->row
[i
][1],
4651 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4652 isl_int_add_ui(qp
->div
->row
[i
][1],
4653 qp
->div
->row
[i
][1], 1);
4655 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4656 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4657 qp
= substitute_div(qp
, i
, s
);
4665 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4666 * a rational division a/m.
4668 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4669 __isl_take isl_pw_qpolynomial
*pwqp
)
4676 if (isl_pw_qpolynomial_is_zero(pwqp
))
4679 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4683 for (i
= 0; i
< pwqp
->n
; ++i
) {
4684 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4691 isl_pw_qpolynomial_free(pwqp
);
4695 /* Adjust all the integer divisions in "qp" such that they are at least
4696 * one over the given orthant (identified by "signs"). This ensures
4697 * that they will still be non-negative even after subtracting (m-1)/m.
4699 * In particular, f is replaced by f' + v, changing f = [a/m]
4700 * to f' = [(a - m v)/m].
4701 * If the constant term k in a is smaller than m,
4702 * the constant term of v is set to floor(k/m) - 1.
4703 * For any other term, if the coefficient c and the variable x have
4704 * the same sign, then no changes are needed.
4705 * Otherwise, if the variable is positive (and c is negative),
4706 * then the coefficient of x in v is set to floor(c/m).
4707 * If the variable is negative (and c is positive),
4708 * then the coefficient of x in v is set to ceil(c/m).
4710 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4716 struct isl_upoly
*s
;
4718 qp
= isl_qpolynomial_cow(qp
);
4721 qp
->div
= isl_mat_cow(qp
->div
);
4725 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4726 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4728 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4729 isl_int
*row
= qp
->div
->row
[i
];
4733 if (isl_int_lt(row
[1], row
[0])) {
4734 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4735 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4736 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4738 for (j
= 0; j
< total
; ++j
) {
4739 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4742 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4744 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4745 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4747 for (j
= 0; j
< i
; ++j
) {
4748 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4750 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4751 row
[2 + total
+ j
], row
[0]);
4752 isl_int_submul(row
[2 + total
+ j
],
4753 row
[0], v
->el
[1 + total
+ j
]);
4755 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4756 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4758 isl_seq_combine(qp
->div
->row
[j
] + 1,
4759 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4760 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4762 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4763 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4764 qp
->div
->ctx
->one
, v
->size
);
4765 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4775 isl_qpolynomial_free(qp
);
4779 struct isl_to_poly_data
{
4781 isl_pw_qpolynomial
*res
;
4782 isl_qpolynomial
*qp
;
4785 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4786 * We first make all integer divisions positive and then split the
4787 * quasipolynomials into terms with sign data->sign (the direction
4788 * of the requested approximation) and terms with the opposite sign.
4789 * In the first set of terms, each integer division [a/m] is
4790 * overapproximated by a/m, while in the second it is underapproximated
4793 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
4794 int *signs
, void *user
)
4796 struct isl_to_poly_data
*data
= user
;
4797 isl_pw_qpolynomial
*t
;
4798 isl_qpolynomial
*qp
, *up
, *down
;
4800 qp
= isl_qpolynomial_copy(data
->qp
);
4801 qp
= make_divs_pos(qp
, signs
);
4803 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4804 up
= qp_drop_floors(up
, 0);
4805 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4806 down
= qp_drop_floors(down
, 1);
4808 isl_qpolynomial_free(qp
);
4809 qp
= isl_qpolynomial_add(up
, down
);
4811 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4812 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4817 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4818 * the polynomial will be an overapproximation. If "sign" is negative,
4819 * it will be an underapproximation. If "sign" is zero, the approximation
4820 * will lie somewhere in between.
4822 * In particular, is sign == 0, we simply drop the floors, turning
4823 * the integer divisions into rational divisions.
4824 * Otherwise, we split the domains into orthants, make all integer divisions
4825 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4826 * depending on the requested sign and the sign of the term in which
4827 * the integer division appears.
4829 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4830 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4833 struct isl_to_poly_data data
;
4836 return pwqp_drop_floors(pwqp
);
4842 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4844 for (i
= 0; i
< pwqp
->n
; ++i
) {
4845 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4846 isl_pw_qpolynomial
*t
;
4847 t
= isl_pw_qpolynomial_alloc(
4848 isl_set_copy(pwqp
->p
[i
].set
),
4849 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4850 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4853 data
.qp
= pwqp
->p
[i
].qp
;
4854 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4855 &to_polynomial_on_orthant
, &data
) < 0)
4859 isl_pw_qpolynomial_free(pwqp
);
4863 isl_pw_qpolynomial_free(pwqp
);
4864 isl_pw_qpolynomial_free(data
.res
);
4868 static __isl_give isl_pw_qpolynomial
*poly_entry(
4869 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4873 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4876 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4877 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4879 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4880 &poly_entry
, &sign
);
4883 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4884 __isl_take isl_qpolynomial
*qp
)
4888 isl_vec
*aff
= NULL
;
4889 isl_basic_map
*bmap
= NULL
;
4895 if (!isl_upoly_is_affine(qp
->upoly
))
4896 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4897 "input quasi-polynomial not affine", goto error
);
4898 aff
= isl_qpolynomial_extract_affine(qp
);
4901 dim
= isl_qpolynomial_get_space(qp
);
4902 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4903 n_div
= qp
->div
->n_row
;
4904 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4906 for (i
= 0; i
< n_div
; ++i
) {
4907 k
= isl_basic_map_alloc_div(bmap
);
4910 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4911 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4912 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4915 k
= isl_basic_map_alloc_equality(bmap
);
4918 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4919 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4920 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4923 isl_qpolynomial_free(qp
);
4924 bmap
= isl_basic_map_finalize(bmap
);
4928 isl_qpolynomial_free(qp
);
4929 isl_basic_map_free(bmap
);